Design and stability of moving horizon estimator for discrete-time linear systems subject to multiple measurement outliers

This paper considers the state estimation problem for discrete-time linear systems suffering from dense measurement anomalies. Conventional moving horizon estimation algorithms can be used to solve the case containing sparse measurement anomalies, but their performance degrades dramatically as the number of outliers increases. To address this problem, we propose two outliers exclusion-moving horizon estimation strategies. That is, at each sampling instant, solving a set of least-squares cost functions aims to exclude all possible outliers. The state estimates corresponding to the optimal cost are retained and propagated to the next instant, and the procedure is repeated when new information arrives. The stability of the estimation error of the estimators is proved under moderate conditions, namely the observability of the noise-free state equation and the choice of the tuning parameters in the cost function. The simulation results demonstrate the robustness of the proposed approaches in the presence of dense outliers.